Our simulations were performed for a translationally invariant
system with equal tunnelings between all lattice sites, where the
ground state is one with a uniform phase. The time needed to
eliminate the vortices from the system is therefore the time that
the system needs to reach the lowest energy state. It has been
suggested to use photon condensates for analog computation by
letting them find the ground state of a nontrivial classical XY
model hamiltonian [1]}. Our insights obtained here on
the annihilation of vortex pairs are expected to be relevant for the
estimation of the time needed to reach the ground state in such
applications and the trends that were observed for the dependence on
the system parameters may be useful in order to improve the
performance of analog computing with photon BECs.
